Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  long long n;
  cin >> n;
  std::vector<long long> v(1e5 + 7);
  for (long long i = 0; i < 1e5 + 7; i++) {
    v[i] = (i + 1) * (i + 2) / 2;
  }
  int flag = 0;
  for (long long i = 0; i < 1e5 + 7; i++) {
    if (binary_search(v.begin(), v.end(), n - v[i])) {
      flag = 1;
      break;
    }
  }
  if (flag)
    cout << "YES" << endl;
  else
    cout << "NO" << endl;
}